# Statistics Assignment Solved Solution Sample

BARCELONA

QUESTION

Assignment The excel file BarcelonaRE.xlsx contains data on prices and characteristics of 413 residential properties in Barcelona (worksheet 413 properties for analysis). Your team assignment is to price additional 200 residential properties in Barcelona whose characteristics are in the Excel file PriceSubmission.xlsx (also included in the worksheet 200 properties to be priced of the BarcelonaRE.xlsx file).

BarcelonaRE.xlsx

Your team score on this assignment will be based on:

a) The average of the squared errors of your price predictions for 200 properties that you need to price. The actual price of each of the 200 properties is known (these 200 properties and 413 properties with prices come from the same dataset) and will be used to determine the average of the squared errors of your predictions. The smaller your average of the squared errors is, the higher your score will be. (15 points max)

b) The quality of your argumentations for your price predictions. (5 points max)

Your submission consists of two parts:

a) YOUR 200 PRICE PREDICTIONS Submit your 200 price predictions following the link on the course webpage. You supposed to work with your team on this assignment but every student has to submit individually. Therefore, it is expected that students on the same team will submit the same price predictions. (However, you may submit different values if you wish to do so.)

The best way to submit your predictions is as follows:

• Enter your predictions in the yellow cells of the Excel file PriceSubmission.xlsx.

• Make sure to keep the original sorting of the data in this file since this allows for the proper processing of your submission.

• Once you have your 200 predictions entered, copy all yellow cells (now with your predictions in there) and paste them in the submission window on the submission form.

• Do not use any formatting and paste only the actual values. Introducing currency symbols and other special formatting tools will created an error in the processing of your submission.

You will get a confirmation e-mail with your submission. Only your last submission is recorded by the system and you will be evaluated based on that submission.

Gasoline Test

Question 1:

Run a simple regression with gasoline consumption as the dependent variable and with a dummy variable for urban households as the only independent variable. Based on the regression output, what is the average gas consumption of urban households? (Select the closest number from the choices below.)

 A. -68.680 B. 68.680 C. 269.842 D. 338.522 E. 407.203

Question 2:

Run a simple regression with gasoline consumption as the dependent variable and with a dummy variable for households that are NOT located in an urban area as the only independent variable. Based on the regression output, what is the average gas consumption of urban households? (Select the closest number from the choices below.)

 A. -68.680 B. 68.680 C. 269.842 D. 338.522 E. 407.203

Question 3:

Based on the two regression outputs above, what is the standard error for the average gasoline consumption of urban households? (Select the closest number from the choices below.)

 A. 4.246 B. 4.659 C. 6.774 D. 8.222 E. 271.466

Question 4:

Run a simple regression with gasoline consumption as the dependent variable and with a dummy variable for young and single households as the only independent variable. Based on the regression output, what is the standard error for the gas consumption of households that do NOT consist of a young and single individual? (Select the closest number from the choices below.)

 A. 3.918 B. 22.621 C. 272.862 D. 272.890 E. 294.779

Question 5:

Run a regression with gasoline consumption as the dependent variable and with a dummy for urban households and a dummy for young and single households as the two independent variables. Based on the regression output, do you have enough confidence to claim that households that consists of a young and single individual consume on average less gasoline than urban households?

 A. Yes B. No C. Cannot answer given the information in the regression output

Question 6:

Run a regression with gasoline consumption as the dependent variable and with a dummy for urban households, a dummy for young and single households, and a dummy for young and single households that live in an urban area as the three independent variables. What is the average gasoline consumption of households that consist of a young and single individual who lives in an urban area? (Select the closest number from the choices below.)

 A. 186.474 B. 190.127 C. 256.988 D. 339.864 E. Cannot answer given the information in the regression output

Gasoline Demand Data

Price Submission xlsx

Barcelona

First of all, we checked the type of variables involved in the equation. The City Zone variable is a character variable, so it won’t play any role in the regression analysis of the price prediction. m2 is an integer variable. Apart from this, rest other variables are the categorical variables.

After that, we performed the correlational analysis between the variables. Most of the correlation were very small, with the high values being around 0.66. So, we need not do a Principal Component Analysis in this case, as the VIF would also be lower. We decided to perform a simple linear regression.

We built the model using the data of 413 cities. We started with 10 variables and continued reducing variables on the basis of the p-value. We eliminated those variables whose p values were greater than 0.05, one by one on the highest order basis. Finally, we built the model with 6 independent variables (m2, Rooms, Bathrooms, Atico, Parking, Yard). We used the same regression line to predict the price for the 213 cities.

BarcelonaRe.xlsx Solution

Gasoline Demand Data

Run a simple regression with gasoline consumption as the dependent variable and with a dummy variable for urban households as the only independent variable. Based on the regression output, what is the average gas consumption of urban households? (Select the closest number from the choices below.)

 A. -68.680 B. 68.680 C. 269.842 D. 338.522 E. 407.203 Ans. C. 269.842

2:

Run a simple regression with gasoline consumption as the dependent variable and with a dummy variable for households that are NOT located in an urban area as the only independent variable. Based on the regression output, what is the average gas consumption of urban households? (Select the closest number from the choices below.)

 A. -68.680 B. 68.680 C. 269.842 D. 338.522 E. 407.203 Ans. D. 338.522

3:

Based on the two regression outputs above, what is the standard error for the average gasoline consumption of urban households? (Select the closest number from the choices below.)

 A. 4.246 B. 4.659 C. 6.774 D. 8.222 E. 271.466 Ans. C. 6.774

4:

Run a simple regression with gasoline consumption as the dependent variable and with a dummy variable for young and single households as the only independent variable. Based on the regression output, what is the standard error for the gas consumption of households that do NOT consist of a young and single individual? (Select the closest number from the choices below.)

 A. 3.918 B. 22.621 C. 272.862 D. 272.890 E. 294.779 Ans. C. 272.862

5:

Run a regression with gasoline consumption as the dependent variable and with a dummy for urban households and a dummy for young and single households as the two independent variables. Based on the regression output, do you have enough confidence to claim that households that consists of a young and single individual consume on average less gasoline than urban households?

 A. Yes B. No C. Cannot answer given the information in the regression output

Ans. We would formulate the null hypothesis as that the average gasoline consumption for young and single individuals is equal to that of the urban households.

Alternate hypothesis will be that the average gasoline consumption for young and single individuals is less than that of urban households.

On performing the regression analysis, and calculating t-statistic, we reject the null hypothesis.

6:

Run a regression with gasoline consumption as the dependent variable and with a dummy for urban households, a dummy for young and single households, and a dummy for young and single households that live in an urban area as the three independent variables. What is the average gasoline consumption of households that consist of a young and single individual who lives in an urban area? (Select the closest number from the choices below.)

 A. 186.474 B. 190.127 C. 256.988 D. 339.864 E. Cannot answer given the information in the regression output

Ans. A. 186.474

Gasoline Demand Data xlsx

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